which equation represents the line that passes through the points (3, 7) and (-1, -1)?
Answers
points: (3, 7) and (-1, -1)
slope (m) :
[tex]\sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]
========
[tex]\hookrightarrow \dfrac{-1-7}{-1-3}[/tex]
[tex]\hookrightarrow \dfrac{-8}{-4}[/tex]
[tex]\hookrightarrow 2[/tex]
Equation:
[tex]\sf y-y_1 = m(x-x_1)[/tex]
==============
[tex]\rightarrow \sf y-7 = 2(x-3)[/tex]
[tex]\rightarrow \sf y = 2x-6+7[/tex]
[tex]\rightarrow \sf y = 2x+1[/tex]
Answer:
[tex]y = 2x- 1[/tex]
Step-by-step explanation:
To determine which equation passes through the points (3, 7) and (-1, -1), we need to determine the slope of the equation. Then, we shall use point slope form to determine the equation of the line.
Determining the slope of the line:
[tex]\text{Slope} = \dfrac{\text{Rise}}{\text{Run} } =\dfrac{\text{y}_{2} - \text{y}_{1} }{\text{x}_{2} - \text{x}_{1} }[/tex]
Substituting the points in the slope formula:
[tex]\text{Slope} =\dfrac{-1 - 7 }{-1- 3 }[/tex]
Simplifying the slope:
[tex]\text{Slope} =\dfrac{-1 - 7 }{-1- 3 }[/tex]
[tex]\text{Slope} =\dfrac{-8}{-4 } = 2[/tex]
Determining the equation of the line:
We shall use point slope form to determine the equation of the line.
[tex]\text{Point slope form:} \ y - y_{1} = m(x- x_{1} )[/tex]
Substitute the slope and the coordinates of any two points stated above.
[tex]y -7= 2(x- 3 ) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Using the point (3,7)}][/tex]
Simplify the equation and organize it to slope intercept form:
[tex]y -7= 2x- 6[/tex]
[tex]y = 2x- 6 + 7[/tex]
[tex]y = 2x+ 1[/tex]
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Answers
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I hope I answered your question!
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have a nice day!
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[tex]y=a(x-h)^2 + k[/tex]
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Step-by-step explanation:
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Answer:
3 (4+13)
Step-by-step explanation:
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1. X=7 and y=3
A. X+Y=
B. X+X+Y=
C. 2X+5Y=
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Answers
Answer:
A. 10
B. 17
C. 29
D. 80
E. 300
Step-by-step explanation:
A.
x + y
7 + 3
10
B.
x + x + y
7 + 7 + 3
14 + 3
17
C.
2x + 5y
2(7) + 5(3)
14 + 15
29
D.
8(x + y)
8(7 + 3)
8(10)
80
E.
15(2x + y + y)
15(2(7) + 3 + 3)
15(14 + 3 + 3)
15(17 + 3)
15(20)
300